The Shapley value of TU games, differences of the cores of convex games, and the Steiner point of convex compact sets

Sergei L. Pechersky

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 3, pp. 58-85.

Résumé

We explore the implications of the possibility of decomposition of any TU game $v$ into the difference of two convex games $v_1$ and $v_2$, i.e. $v=v_1-v_2.$ In particular, we prove that the Shapley value of a game $v$ is the difference of the Steiner points of the cores $C(v_1)$ and $C(v_2),$ and, in particular, for a convex game $v$ the Shapley value is the Steiner point of its core. Some properties of this interpretation are studied. A new definition of the Weber set of a TU game is considered.

Détail

Keywords: TU games, convex games, the Shapley value, the Steiner point, differences of the cores.

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